Properties

Label 139650gd
Number of curves $4$
Conductor $139650$
CM no
Rank $0$
Graph

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Show commands for: SageMath
sage: E = EllipticCurve("139650.cr1")
 
sage: E.isogeny_class()
 

Elliptic curves in class 139650gd

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients Torsion structure Modular degree Optimality
139650.cr4 139650gd1 [1, 0, 1, -12276, -894302] [2] 663552 \(\Gamma_0(N)\)-optimal
139650.cr3 139650gd2 [1, 0, 1, -232776, -43230302] [2, 2] 1327104  
139650.cr2 139650gd3 [1, 0, 1, -269526, -28677302] [2] 2654208  
139650.cr1 139650gd4 [1, 0, 1, -3724026, -2766405302] [2] 2654208  

Rank

sage: E.rank()
 

The elliptic curves in class 139650gd have rank \(0\).

Modular form 139650.2.a.cr

sage: E.q_eigenform(10)
 
\( q - q^{2} + q^{3} + q^{4} - q^{6} - q^{8} + q^{9} - 4q^{11} + q^{12} - 2q^{13} + q^{16} - 2q^{17} - q^{18} + q^{19} + O(q^{20}) \)

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.